TY - JOUR
T1 - Volume rigidity and algebraic shifting
AU - Bulavka, Denys
AU - Nevo, Eran
AU - Peled, Yuval
N1 - Publisher Copyright:
© 2024 Elsevier Inc.
PY - 2025/1
Y1 - 2025/1
N2 - We study the generic volume-rigidity of (d−1)-dimensional simplicial complexes in Rd−1, and show that the volume-rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume-rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions >1, volume-rigidity is not characterized by a corresponding hypergraph sparsity property.
AB - We study the generic volume-rigidity of (d−1)-dimensional simplicial complexes in Rd−1, and show that the volume-rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume-rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions >1, volume-rigidity is not characterized by a corresponding hypergraph sparsity property.
KW - Algebraic Shifting
KW - Rigidity theory
KW - Simplicial Complexes
UR - http://www.scopus.com/inward/record.url?scp=85204953866&partnerID=8YFLogxK
U2 - 10.1016/j.jctb.2024.09.002
DO - 10.1016/j.jctb.2024.09.002
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AN - SCOPUS:85204953866
SN - 0095-8956
VL - 170
SP - 189
EP - 202
JO - Journal of Combinatorial Theory. Series B
JF - Journal of Combinatorial Theory. Series B
ER -